w^2+70w-300=0

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Solution for w^2+70w-300=0 equation:


Simplifying
w2 + 70w + -300 = 0

Reorder the terms:
-300 + 70w + w2 = 0

Solving
-300 + 70w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 70w + 300 + w2 = 0 + 300

Reorder the terms:
-300 + 300 + 70w + w2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 70w + w2 = 0 + 300
70w + w2 = 0 + 300

Combine like terms: 0 + 300 = 300
70w + w2 = 300

The w term is 70w.  Take half its coefficient (35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
70w + 1225 + w2 = 300 + 1225

Reorder the terms:
1225 + 70w + w2 = 300 + 1225

Combine like terms: 300 + 1225 = 1525
1225 + 70w + w2 = 1525

Factor a perfect square on the left side:
(w + 35)(w + 35) = 1525

Calculate the square root of the right side: 39.05124838

Break this problem into two subproblems by setting 
(w + 35) equal to 39.05124838 and -39.05124838.

Subproblem 1

w + 35 = 39.05124838 Simplifying w + 35 = 39.05124838 Reorder the terms: 35 + w = 39.05124838 Solving 35 + w = 39.05124838 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + w = 39.05124838 + -35 Combine like terms: 35 + -35 = 0 0 + w = 39.05124838 + -35 w = 39.05124838 + -35 Combine like terms: 39.05124838 + -35 = 4.05124838 w = 4.05124838 Simplifying w = 4.05124838

Subproblem 2

w + 35 = -39.05124838 Simplifying w + 35 = -39.05124838 Reorder the terms: 35 + w = -39.05124838 Solving 35 + w = -39.05124838 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + w = -39.05124838 + -35 Combine like terms: 35 + -35 = 0 0 + w = -39.05124838 + -35 w = -39.05124838 + -35 Combine like terms: -39.05124838 + -35 = -74.05124838 w = -74.05124838 Simplifying w = -74.05124838

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.05124838, -74.05124838}

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